Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity
Abstract The hybrid metric-Palatini $$f({\mathscr {R}})$$ f(R) gravity is a recently devised approach to modified gravity in which it is added to the metric Ricci scalar R, in the Einstein–Hilbert Lagrangian, a function $$f({\mathscr {R}})$$ f(R) of Palatini curvature scalar $${\mathscr {R}}$$ R , w...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
SpringerOpen
2018-07-01
|
Series: | European Physical Journal C: Particles and Fields |
Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-018-6025-4 |
id |
doaj-64c1e3b59c1b4e1c91203a3483a28979 |
---|---|
record_format |
Article |
spelling |
doaj-64c1e3b59c1b4e1c91203a3483a289792020-11-25T01:15:05ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522018-07-0178711010.1140/epjc/s10052-018-6025-4Homogeneous Gödel-type solutions in hybrid metric-Palatini gravityJ. Santos0M. J. Rebouças1A. F. F. Teixeira2Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do NorteCentro Brasileiro de Pesquisas FísicasCentro Brasileiro de Pesquisas FísicasAbstract The hybrid metric-Palatini $$f({\mathscr {R}})$$ f(R) gravity is a recently devised approach to modified gravity in which it is added to the metric Ricci scalar R, in the Einstein–Hilbert Lagrangian, a function $$f({\mathscr {R}})$$ f(R) of Palatini curvature scalar $${\mathscr {R}}$$ R , which is constructed from an independent connection. These hybrid metric-Palatini gravity theories provide an alternative way to explain the current accelerating expansion without a dark energy matter component. If gravitation is to be described by a hybrid metric-Palatini $$f({\mathscr {R}})$$ f(R) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality. Here, to look further into the potentialities and difficulties of $$f({\mathscr {R}})$$ f(R) theories, we examine whether they admit Gödel-type solutions for physically well-motivated matter source. We first show that under certain conditions on the matter sources the problem of finding out space-time homogeneous (ST-homogeneous) solutions in $$f({\mathscr {R}})$$ f(R) theories reduces to the problem of determining solutions of Einstein’s field equations with a cosmological constant. Employing this far-reaching result, we determine a general ST-homogeneous Gödel-type solution whose matter source is a combination of a scalar with an electromagnetic fields plus a perfect fluid. This general Gödel-type solution contains special solutions in which the essential parameter $$m^2$$ m2 can be $$m^{2} > 0$$ m2>0 hyperbolic family, $$m=0$$ m=0 linear class, and $$m^{2} < 0$$ m2<0 trigonometric family, covering thus all classes of homogeneous Gödel-type spacetimes. This general solution also contains all previously known solutions as special cases. The bare existence of these Gödel-type solutions makes apparent that hybrid metric-Palatini $$f({\mathscr {R}})$$ f(R) gravity does not remedy causal anomaly in the form of closed timelike curves that are permitted in general relativity.http://link.springer.com/article/10.1140/epjc/s10052-018-6025-4 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
J. Santos M. J. Rebouças A. F. F. Teixeira |
spellingShingle |
J. Santos M. J. Rebouças A. F. F. Teixeira Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity European Physical Journal C: Particles and Fields |
author_facet |
J. Santos M. J. Rebouças A. F. F. Teixeira |
author_sort |
J. Santos |
title |
Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity |
title_short |
Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity |
title_full |
Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity |
title_fullStr |
Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity |
title_full_unstemmed |
Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity |
title_sort |
homogeneous gödel-type solutions in hybrid metric-palatini gravity |
publisher |
SpringerOpen |
series |
European Physical Journal C: Particles and Fields |
issn |
1434-6044 1434-6052 |
publishDate |
2018-07-01 |
description |
Abstract The hybrid metric-Palatini $$f({\mathscr {R}})$$ f(R) gravity is a recently devised approach to modified gravity in which it is added to the metric Ricci scalar R, in the Einstein–Hilbert Lagrangian, a function $$f({\mathscr {R}})$$ f(R) of Palatini curvature scalar $${\mathscr {R}}$$ R , which is constructed from an independent connection. These hybrid metric-Palatini gravity theories provide an alternative way to explain the current accelerating expansion without a dark energy matter component. If gravitation is to be described by a hybrid metric-Palatini $$f({\mathscr {R}})$$ f(R) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality. Here, to look further into the potentialities and difficulties of $$f({\mathscr {R}})$$ f(R) theories, we examine whether they admit Gödel-type solutions for physically well-motivated matter source. We first show that under certain conditions on the matter sources the problem of finding out space-time homogeneous (ST-homogeneous) solutions in $$f({\mathscr {R}})$$ f(R) theories reduces to the problem of determining solutions of Einstein’s field equations with a cosmological constant. Employing this far-reaching result, we determine a general ST-homogeneous Gödel-type solution whose matter source is a combination of a scalar with an electromagnetic fields plus a perfect fluid. This general Gödel-type solution contains special solutions in which the essential parameter $$m^2$$ m2 can be $$m^{2} > 0$$ m2>0 hyperbolic family, $$m=0$$ m=0 linear class, and $$m^{2} < 0$$ m2<0 trigonometric family, covering thus all classes of homogeneous Gödel-type spacetimes. This general solution also contains all previously known solutions as special cases. The bare existence of these Gödel-type solutions makes apparent that hybrid metric-Palatini $$f({\mathscr {R}})$$ f(R) gravity does not remedy causal anomaly in the form of closed timelike curves that are permitted in general relativity. |
url |
http://link.springer.com/article/10.1140/epjc/s10052-018-6025-4 |
work_keys_str_mv |
AT jsantos homogeneousgodeltypesolutionsinhybridmetricpalatinigravity AT mjreboucas homogeneousgodeltypesolutionsinhybridmetricpalatinigravity AT affteixeira homogeneousgodeltypesolutionsinhybridmetricpalatinigravity |
_version_ |
1725154549992259584 |